Arctan Calculator - Mathematical Calculations & Solutions
How It Works
Enter Value
Input number or coordinates
Calculate Arctan
Apply inverse tangent
Common Examples
Understanding Arctan Calculator
What is Arctan?
Arctan is the inverse tangent function. It finds the angle when you know the tangent value. This calculator helps you find angles from ratios quickly and accurately.
Why Use This Tool?
Perfect for students, engineers, and professionals. Solve trigonometry problems, calculate slopes, find angles in triangles, and work with coordinate systems.
Real Applications
Used in computer graphics, robotics, navigation, physics calculations, engineering design, and mathematical problem solving.
Step-by-Step Examples
| Input Value | Formula Used | Result | Common Use |
|---|---|---|---|
| x = 1 | arctan(1) | 45° (π/4 rad) | 45-degree angles |
| x = 0 | arctan(0) | 0° (0 rad) | Horizontal lines |
| x = √3 ≈ 1.732 | arctan(√3) | 60° (π/3 rad) | Equilateral triangles |
| y=3, x=4 | atan2(3, 4) | 36.87° | Coordinate angles |
| x = 0.5 | arctan(0.5) | 26.57° | Slope calculations |
| x = 1/√3 ≈ 0.577 | arctan(1/√3) | 30° (π/6 rad) | 30-60-90 triangles |
Basic Arctan Function
The basic arctan function takes one input value and returns an angle. This is perfect when you know the tangent ratio and need to find the angle.
Range: -90° to +90° (-π/2 to +π/2 radians)
Two-Argument Atan2
The atan2 function takes two arguments (y, x) and gives you the full 360-degree range. This is useful for coordinate systems and navigation.
Range: -180° to +180° (-π to +π radians)
Practical Applications of Arctan
📐 Engineering & Construction
Calculate roof slopes, ramp angles, and structural inclinations. Find the angle of elevation for stairs, bridges, and building designs.
🧭 Navigation & GPS
Determine bearing angles between two points. Calculate direction angles for navigation systems and GPS coordinates.
🎮 Computer Graphics
Rotate objects, calculate camera angles, and determine sprite orientations in games and 3D modeling software.
🤖 Robotics & Automation
Control robot arm movements, calculate joint angles, and determine optimal paths for autonomous vehicles.
📊 Physics & Science
Analyze projectile motion, calculate wave phases, and determine force vector directions in physics experiments.
📚 Education & Learning
Solve trigonometry homework, understand triangle relationships, and learn inverse trigonometric functions step by step.
Mathematical Properties & Formulas
Key Properties
- •Domain: All real numbers (-∞, +∞)
- •Range: -π/2 to π/2 (-90° to 90°)
- •Odd function: arctan(-x) = -arctan(x)
- •Continuous: No breaks or jumps
- •Monotonic: Always increasing
Important Identities
Common Mistakes to Avoid
❌ Wrong: Confusing Degrees and Radians
Always check if your calculator is in the right mode. Most programming languages use radians by default.
✅ Correct: Check Your Units
Always convert between degrees and radians when needed. Use our calculator's unit selector.
❌ Wrong: Using Arctan for Full Circle
Basic arctan only gives -90° to 90°. For full 360° range, use atan2 function.
✅ Correct: Use Atan2 for Coordinates
When working with coordinates, use atan2(y,x) to get the correct quadrant.
Frequently Asked Questions About Arctan Calculator
What is arctan (arctangent) and how does it work?
Arctan is the inverse tangent function that finds the angle when you know the tangent value. If tan(θ) = x, then arctan(x) = θ. It's written as arctan(x), tan⁻¹(x), or atan(x). This function is essential for finding angles in right triangles when you know the opposite and adjacent sides.
What's the difference between arctan and atan2?
Arctan(x) takes one argument and returns angles from -90° to 90° (two quadrants). Atan2(y,x) takes two arguments and returns angles from -180° to 180° (all four quadrants). Use atan2 when you need to determine which quadrant the angle is in, especially for coordinate systems and navigation.
What is the range and domain of arctan?
The domain of arctan is all real numbers (-∞ to +∞). The range is from -π/2 to π/2 radians (or -90° to 90°). This means arctan can accept any number as input but will only output angles in the first and fourth quadrants.
When should I use atan2 instead of basic arctan?
Use atan2(y,x) when working with coordinates, navigation systems, robotics, or computer graphics where you need the full 360° range. It's especially important when the x-coordinate might be zero (which would cause division by zero in arctan(y/x)) or when you need to distinguish between opposite quadrants.
What are the most common arctan values I should memorize?
Key values: arctan(0) = 0°, arctan(1/√3) = 30°, arctan(1) = 45°, arctan(√3) = 60°. Also useful: arctan(∞) = 90°, arctan(-1) = -45°. These correspond to common angles in 30-60-90 and 45-45-90 triangles, making them essential for trigonometry.
How do I convert between radians and degrees?
To convert radians to degrees: multiply by 180/π. To convert degrees to radians: multiply by π/180. Our calculator shows both units automatically. Remember: π radians = 180°, so π/2 rad = 90°, π/4 rad = 45°, etc.
What are practical applications of arctan in real life?
Arctan is used in engineering (calculating slopes and angles), navigation (bearing calculations), robotics (joint angles), computer graphics (rotations), physics (projectile motion), architecture (roof pitches), and surveying (elevation angles). It's essential whenever you need to find an angle from a ratio.
How accurate is this arctan calculator?
Our calculator uses JavaScript's built-in Math.atan() and Math.atan2() functions, which provide double-precision floating-point accuracy (about 15-17 decimal digits). This is more than sufficient for most practical applications, from homework problems to professional engineering calculations.
Can I use this calculator for homework and exams?
Yes! This calculator is perfect for checking your work on trigonometry homework, physics problems, and engineering calculations. However, always check your instructor's policy on calculator use during exams. The step-by-step explanations help you understand the process, not just get answers.
What should I do if I get unexpected results?
First, check if you're using the right function (arctan vs atan2) and the correct units (degrees vs radians). Make sure your input values are correct. If calculating arctan(y/x), consider using atan2(y,x) instead to avoid division by zero and get the correct quadrant. Remember that arctan has a limited range of -90° to 90°.
Learn More About Trigonometry
📚 Study Tips
- • Practice with unit circle
- • Memorize common angles
- • Understand inverse functions
- • Draw right triangles
🔗 Related Functions
- • Arcsin (inverse sine)
- • Arccos (inverse cosine)
- • Tangent function
- • Hyperbolic functions
💡 Quick Facts
- • Arctan is continuous everywhere
- • It's an odd function
- • Has horizontal asymptotes
- • Derivative: 1/(1+x²)
Why Choose Our Arctan Calculator?
✅ Features & Benefits:
- • Instant calculations with high precision
- • Both basic arctan and atan2 functions
- • Automatic degree/radian conversion
- • Step-by-step explanations
- • Mobile-friendly responsive design
- • No registration or downloads required
- • Completely free to use
🎯 Perfect For:
- • Students learning trigonometry
- • Engineers and architects
- • Programmers and developers
- • Physics and math teachers
- • Navigation and GPS applications
- • Robotics and automation
- • Computer graphics and gaming